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I want to know how neuroscientists use mathematics to describe memory in living creatures. How do neuroscientists model memory and show how it works by mathematics?

I am a theoretical physics PhD student, and interested in neuroscience too. The only tool which I have and I could use to study neuroscience is mathematics and programing. That's why I want to know how neuroscientists address the memory by mathematics. I know how math works to describe neurons oscillations and action potential, but I don't know how it works for memory.

The cellular models of memory involve plenty of math but those models are only half the story. At the psychological level, we know a lot more about memory as a phenomenon but that knowledge is not encapsulated by any grand formal model. In any case, here are the mathematical models of plasticity which is thought to be a mechanism underlying memory formation. scholarpedia.org/article/Models_of_synaptic_plasticity
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jeradFeb 18 '14 at 19:07

Small wonder that more recent work resembles Atkinson & Shiffrin's (1965) model. Like I said, it's a classic! I've added your link as another example of artificial neural network models. May have to turn this into a community wiki before long!
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Nick StaunerMar 13 '14 at 23:03

If you have a physics background, you may be particularly interested in Sparse Distributed Memory, a model that provides a number of psychologically plausible characteristics, and is also neuroscientifically plausible.

The model and some of its characteristics are summarized in this paper.

Many great references have been provided by Nick Stauner (and I can't comment there for lack of reputation), but this model is, in my view, one of the most promising and comprehensive ones in Cognitive Science.

Memory is a big word. Usually, neuroscientists and psychologists will try to model a specific cognitive process: for example, long-term recognition memory (the ability to distinguish between previously learned items and new items). Here is a link to a very good introductory text in computational neuroscience (which includes a section about memory and learning): http://grey.colorado.edu/CompCogNeuro/index.php?title=CCNBook/Main